https://github.com/ray-chew/modified_ch

Density functional theory (DFT) and self-consistent field theory (SCFT) simulation of diblock copolymers
https://github.com/ray-chew/modified_ch

cuda density-functional-theory diblock-copolymer numerical-analysis numerical-methods self-consistent-field-theory

Last synced: about 1 month ago
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Density functional theory (DFT) and self-consistent field theory (SCFT) simulation of diblock copolymers

• Host: GitHub
• URL: https://github.com/ray-chew/modified_ch
• Owner: ray-chew
• License: mpl-2.0
• Created: 2018-03-29T09:49:19.000Z (almost 7 years ago)
• Default Branch: master
• Last Pushed: 2024-03-19T09:54:31.000Z (11 months ago)
• Last Synced: 2024-11-12T14:13:43.946Z (3 months ago)
• Topics: cuda, density-functional-theory, diblock-copolymer, numerical-analysis, numerical-methods, self-consistent-field-theory
• Language: Jupyter Notebook
• Homepage:
• Size: 31.1 MB
• Stars: 0
• Watchers: 0
• Forks: 0
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# modified_ch

This repository contains code that solves:

1. The Ohta-Kawasaki / modified Cahn-Hilliard equation used in Density Functional Theory (DFT) and

2. the modified diffusion / Fokker-Planck equation used in Self-Consistent Field Theory (SCFT).

The chapters below refer to where the results appear in my Master's thesis (available upon request).

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- DFT numerics (Chapter 4, 7):

    1. *1D_Lie_SSP_RK2.ipynb* - 1D DFT scheme based on Lie-splitting involving a Fourier pseudospectral method, and strong-stability preserving 2nd-order accurate Runge-Kutta (SSP-RK3) time-stepping with a 2nd-order accurate central difference scheme.

    2. *2D_Strang_SSP_RK3.ipynb* - 2D DFT scheme based on a Strang-splitting involving two Fourier-PS methods, a 3rd-order SSP-RK3, and a 4th-order accurate central difference scheme.

- SCFT numerics (Chapters 6, 7):

    1. *1D_SCFT* - 1D SCFT scheme based on the paper published by [Rasmussen and Kalosakas (2002)](https://onlinelibrary.wiley.com/doi/abs/10.1002/polb.10238).

    2. *2D_SCFT* - 2D SCFT scheme.

    

- Benchmarking (Appendix F):

    1. *GPU_test.ipynb* - Compares computational costs of CPU- and GPU-based methods. Used alongside *EOC.ipynb* for calculating the order of convergence for the 2D DFT scheme in Chapter 4, Section 4.3.

- Misc:

    1. *lsa.nb* - Mathematica code for calculating the theoretical DFT order-disorder curves.

    2. *Pts1.csv*, *Pts2.csv* - Data points of the theoretical DFT curves.

    3. *SCFT_Us_XN_10-15_V_1-9* and *DFT_Us_delta_0.40-0.64_V_1.0-23.8* - Output of the data arrays used to plot the scatter plots of figure 7.5 (comparison of DFT and SCFT equilibrium homogeneous lamellar periodicity).

    4. *detect_peaks.py* - Peak counter from [here](https://github.com/demotu/BMC/blob/master/functions/detect_peaks.py).

    5. *uArrs* - Various output arrays used in determining the order of convergence of the 2D DFT numerical scheme in chapter 4, section 4.3.

    6. *ETDRK4* - Archived code. An attempt at the 1D exponential time-differencing 4th-order accurate Runge-Kutta method. See [Kassam and Trefethen (2005)](https://people.maths.ox.ac.uk/trefethen/publication/PDF/2005_111.pdf) for more details. The method works for small enough time steps.

    7. *Lie_Adam-Bashforth* - My first attempt at the DFT numerical scheme. It works in 1D, 2D, and 3D. However, the stability analysis of this scheme is not easy.